- Hi,

I have a question which is related to factoring composite numbers,

although why may not be obvious at first.

I have a (straight) line x1,y1 to x2,y2 where x1 and x2 are whole

numbers and y1 and y2 are not.

My question is, can I calculate the first time the line intersects an

x,y coordinate where both x and y are whole numbers.

Kevin. - Hi Kevin,

This shouldn't be too hard.

simply shift your x,y axis

so that (x1,y1)=(0,0)

you can then express your line as

y=mx (m=y2/x2)

multiply by appropriate numberq so that qy2 and qx2 are integer

let x=qx2 and you will get an iteger y

shift you axes back.

e.g

x1=1, y1=2

x2=5/2 y2=13/3

shift axes

x1=0,y1=0

x2=3/2,y2=7/3

y= (7/3)/(3/2)x

y= (14/9)x

x=9 ==> y=14

shift back (i.e add 1 to x and 2 to y)

x=10,y=16 are integer cordinates on the line that pases through

(1,2) and (2.5,4.3...)

Hope this helps

Cheers

Ken

--- In primenumbers@yahoogroups.com, "Kevin Acres" <research@r...>

wrote:> Hi,

an

>

> I have a question which is related to factoring composite numbers,

> although why may not be obvious at first.

>

> I have a (straight) line x1,y1 to x2,y2 where x1 and x2 are whole

> numbers and y1 and y2 are not.

>

> My question is, can I calculate the first time the line intersects

> x,y coordinate where both x and y are whole numbers.

>

> Kevin.